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Quantum Fingerprinting: Difference between revisions
→Pseudocode
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==Pseudocode== | ==Pseudocode== | ||
'''Stage 1''': Client's preparation</br> | |||
'''Input''': <math>{x \in \{0, 1\}^n}, {y \in \{0, 1\}^n}</math> for first client and second client respectively. </br> | '''Input''': <math>{x \in \{0, 1\}^n}, {y \in \{0, 1\}^n}</math> for first client and second client respectively. </br> | ||
'''Output''': <math>|h_x\rangle</math>, <math>|h_y\rangle</math> sent to server | '''Output''': <math>|h_x\rangle</math>, <math>|h_y\rangle</math> sent to server | ||
* First client prepares <math>|h_x\rangle</math> from <math>x</math>, <math>|h_x\rangle = \frac{1}{\sqrt{m}}\sum_{i=1}^{m} |i\rangle|E_i(x)\rangle</math> | * First client prepares <math>|h_x\rangle</math> from <math>x</math>, <math>|h_x\rangle = \frac{1}{\sqrt{m}}\sum_{i=1}^{m} |i\rangle|E_i(x)\rangle</math> | ||
* Second client prepares <math>|h_y\rangle</math> from <math>y</math>, <math>|h_y\rangle = \frac{1}{\sqrt{m}}\sum_{i=1}^{m} |i\rangle|E_i(y)\rangle</math> | * Second client prepares <math>|h_y\rangle</math> from <math>y</math>, <math>|h_y\rangle = \frac{1}{\sqrt{m}}\sum_{i=1}^{m} |i\rangle|E_i(y)\rangle</math> | ||
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'''Stage 2''': Server's test | '''Stage 2''': Server's test | ||
'''Input''': <math>|h_x\rangle</math>, <math>|h_y\rangle</math> </br> | |||
'''Output''': SWAP test result | |||
* Server prepares an ancilla qubit <math>|0\rangle</math> for SWAP test and starts with state <math>|0\rangle|h_x\rangle|h_y\rangle</math> | * Server prepares an ancilla qubit <math>|0\rangle</math> for SWAP test and starts with state <math>|0\rangle|h_x\rangle|h_y\rangle</math> | ||
* Server applies gate <math>G = {(H\otimes I)(c-SWAP)(H\otimes I)}</math>, resulting in final state <math>\frac{1}{2}|0\rangle(|h_x\rangle|h_y\rangle + |h_y\rangle|h_x\rangle) + \frac{1}{2}|1\rangle(|h_x\rangle|h_y\rangle - |h_y\rangle|h_x\rangle)</math> | * Server applies gate <math>G = {(H\otimes I)(c-SWAP)(H\otimes I)}</math>, resulting in final state <math>\frac{1}{2}|0\rangle(|h_x\rangle|h_y\rangle + |h_y\rangle|h_x\rangle) + \frac{1}{2}|1\rangle(|h_x\rangle|h_y\rangle - |h_y\rangle|h_x\rangle)</math> | ||